Gyrotron travelling-wave amplifier

ABSTRACT

An apparatus for amplifying coherent radiation at millimeter and submillimeter wavelengths includes the combination of a travelling-wave-tube cyclotron-maser-amplifier structure and a magnetron-injection electron gun. The amplifier structure includes a fast-wave drift tube and an electromagnetic wave launcher within the bore of a superconducting magnet. The magnetron-injection electron gun is also within the bore of the magnet and is coupled to the drift tube. As a travelling wave is launched in a preferred mode in the drift tube, the electron gun injects an annular beam of relativistic electrons having both large energy transverse to the axis of the device and small energy spread into the drift tube so that the electrons gyrate at their cyclotron frequency in orbits about the lines of the axial magnetic field produced by the magnet. The travelling wave is amplified by extracting energy from the relativistic electron beam. Efficiency of this energy transfer is optimized by tapering the magnetic field near the output end of the wave-beam interaction region.

BACKGROUND OF THE INVENTION

This invention relates to a microwave amplifier and especially to atravelling-wave amplifier of coherent radiation at millimeter andsubmillimeter wavelengths.

Existing microwave amplifiers, such as conventional travelling wavetubes, are slow-wave devices having periodic structures of certaindimensions such that the structures are in resonance with the wave whichis to be amplified. Thus, the physical size of the periodic structuresmust be varied in order to amplify waves of different frequencies. Thisfeature limits both the tunability of conventional amplifiers and theability of such amplifiers to accommodate high power as the wavelengthbecomes very small because smaller wavelengths require amplifiers withsmaller, more delicate, periodic structures. Therefore, the power levelof these devices falls sharply at millimeter and submillimeterwavelengths.

SUMMARY OF THE INVENTION

It is the general purpose and object of the present invention to providean amplifier of millimeter and submillimeter wavelength radiation whichis characterized by wide tunability, high power levels, wide bandwidth,and good efficiency. This and other objects of the present invention areaccomplished by the combination of a magnetron-injection electron gunand a travelling-wave-tube cyclotron-maser-amplifier structure. Theamplifier structure has a fast-wave drift tube, a launcher forelectromagnetic waves, and a superconducting magnet, but no resonantcavities or periodic structures. The electron gun and wave launcher arecoupled to the drift tube within the bore of the magnet to propagateboth an annular electron beam, in which the electrons gyrate incyclotron orbits about the lines of an axial magnetic field, and atravelling wave.

A travelling wave of chosen frequency ω and chosen waveguide mode islaunched in the drift tube. The injection gun provides a hollow circularbeam of relativistic electrons having both large energy transverse tothe axis of the device and small energy spread. The electrons gyrate intheir orbits within the drift tube at a cyclotron frequency ω_(ce)=qB_(zo) /m, where q and m are the charge and relativistic mass,respectively, of an electron, and B_(zo) is the strength of the appliedmagnetic field about the drift tube. The gyrating electrons transferenergy to the travelling wave when ω is slightly higher than ω_(ce)+k_(z) v_(z) where k_(z) is the axial wave number of the electromagneticwave and v_(z) is the axial velocity of the electrons.

An advantage of the invention is that amplification is a function of thecyclotron frequency ω_(ce) of the device which is determined by theapplied magnetic field and the relativistic mass of the electrons, andnot by the dimensions of a resonant structure. Therefore, no resonantcavities nor periodic structures are employed and the device can operateat very high power levels with wide bandwidth and very wide tunability.Thus, unlike most other microwave amplifier tubes, the internaldimensions of the device may be large compared to the wavelength, andusage at high power is compatible with operation at millimeter andsubmillimeter wavelengths.

Another advantage of the invention is that a tapered magnetic field nearthe end of the wave-electron beam interaction region maximizesefficiency.

Other objects and advantages of the invention will become apparent fromthe following detailed description of the invention when considered inconjunction with the accompanying drawings wherein:

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a cutaway sectional view of an illustrative embodiment of thepresent invention.

FIG. 2 is a graph of axial magnetic field versus distance in the deviceof FIG. 1.

FIG. 3 is a cross-sectional view taken along the line 3--3 of FIG. 1 andshows a TE₀₁ ⁰ wave launched in the circular drift tube by thecombination of TE₁₀.sup.□ waves from two rectangular waveguides havingequal magnitude but opposite phase.

FIG. 4 is a cutaway schematic view showing the electrons gyrating aboutthe axial magnetic field.

FIGS. 5A and 5B are cross-sectional views of the electron beam shown inFIG. 4 taken along the line 5--5 and show the phase synchronism betweenthe electron orbits and the TE₀₁ ⁰ wave on alternate half cycles of theazimuthal electric field E within the circular drift tube.

FIG. 6 is a graph showing operating parameters optimized for maximumefficiency for a selected electron beam velocity ratio α (transversevelocity to axial velocity) of 1.5, a travelling wave in the TE₀₁ ⁰mode, and operating near the fundamental cyclotron frequency.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a travelling-wave-tube cyclotron-maser-amplifier structurecomprising a fast wave drift tube 10 of circular cross-section coupledto two input feed waveguides 12 of rectangular cross-sectionconveniently situated within the bore of a superconducting solenoid 14.A magnetron injection electron gun 16 extends into the bore of thesolenoid 14 and suitably couples to the drift tube 10. The bore of thesolenoid 14 is coaxial with the bore of a dewar 18 so that the electrongun 16, drift tube 10 and waveguides 12 are conveniently inserted intothe bore of the dewar 18 which holds the solenoid 14. The electron gunconnects to a modulator which supplies the required operating voltagesand currents. The input feed waveguides 12 are connected to a source ofcoherent electromagnetic radiation, such as a microwave oscillator. Themodulator, radiation source, and drift tube output are typically locatedexternal to the dewar 18. Liquid helium within the dewar 18 convenientlysurrounds and cools the solenoid 14. The dewar 18 is made of a material,such as non-magnetic stainless steel, which is suitable for theconfiguration herein described and which will hold the liquid helium.

The drift tube 10 and each waveguide 12 are fabricated from standardwaveguide material. The waveguides 12 are suitably coupled to the drifttube 10 at points approximately 180° diametrically apart. The regionwithin the drift tube 10 is evacuated to a vacuum of about 10⁻⁸ Torrwhich is standard for microwave tubes, and is separated from theradiation source by a pressure window 20 typically located within eachwaveguide 12 at a point near the intersection with the drift tube.

The electron gun 16 has a thermionic cathode 22, an intermediatebeam-forming electrode 24, and an anode 26 whose contours and voltagesare chosen together with the contour of the magnetic field from thesolenoid 14, to produce and propagate an annular electron beam with bothlarge energy transverse to the axis of the gun and small energy spread,in which beam the electrons gyrate at a cyclotron frequency in orbitsaround the lines of the magnetic field, and in which beam the velocityratio α of the electrons, that is, the ratio of transverse electronvelocity V.sub.⊥, to axial electron velocity V_(z), is preferably in therange 1.5<α<2.5.

The outer circumference of the portion of the drift tube 10 extendingapproximately externally of the core of the solenoid 14 is an electronbeam collector 28 which is designed to collect the spent electrons anddissipate the resulting heat. The drift tube 10 has a deflection magnet30 located just prior to an output pressure window 32 which terminatesthe drift tube. A conical microwave absorber 34, formed from standardmaterial which absorbs microwave energy in a high vacuum, is locatedwithin the drift tube 10 close to the point of coupling with theelectron gun. The absorber 34 suppresses feedback oscillations.Amplification is optimum in the TE₀₁ ⁰ mode, but operation of the deviceis possible with other waveguides modes, with drift tubes ofnon-circular cross-section, and with other types at wave launchers.

The solenoid 14 provides a magnetic field in the region of the electrongun 16 and drift tube 10. A graph of the strength, with axial distance,of the axial component B_(zo) of the magnetic field about the electrongun 16 and drift tube 10 is shown in FIG. 2. The compression region ofthe magnetic field comprises a radial component B_(rg) and an axialcomponent B_(zg). As an annular electron beam is emitted at relativisticspeeds from the thermionic cathode 22 toward the intermediate electrode24, the radial component B_(rg) and the axial component B_(zg) of themagnetic field cause the electrons to form cyclotron orbits transverseto the axis of the device. The compression region of the magnetic fieldcompresses the beam to provide an inward velocity component and thus toform the electron velocity ratio α as the beam propagates through theanode 26 and into the drift tube 10. After being compressed, the beamenters a region of uniform magnetic field B_(zo) within the drift tube10.

A signal of selected frequency ω from the radiation source propagatesthrough each waveguide 12 as a TE₁₀.sup.□ wave of equal amplitude andopposite phase, as shown in FIG. 3, to launch a TE₀₁ ⁰ wave whichpropagates in the drift tube 10 in a direction toward the outputpressure window 32. The beam, comprising bunches 36 of relativisticelectrons, propagates in the drift tube 10 in the same direction as theTE₀₁ ⁰ wave in the presence of the axial magnetic field, such that theelectrons gyrate in cyclotron orbits at a cyclotron frequency ω_(ce)about the lines of the magnetic field, see FIG. 4. The beam interactswith the TE₀₁ ⁰ wave and amplifies the wave as the beam and wavepropagate.

Initially, the phases of the electrons in their cyclotron orbits arerandom, but phase-bunching occurs because of the relativistic change ofmass of the electrons. Those electrons that lose energy to the wavebecome lighter and accumulate phase-lead while those electrons that gainenergy from the wave become heavier and accumulate phase-lag.Phase-bunching results and the electrons radiate coherently in bunches36 and amplify the wave.

The bunched electrons 36 are distributed around the electron beam radiusr_(o), while gyrating in the cyclotron orbits of radius r_(L) wherer_(L) is typically much smaller than r_(o) as depicted in FIGS. 5A andB. These figures show the phase synchronism between the electron orbitsand the electric field E of the TE₀₁ ⁰ wave on alternate half-cycles,assuming that the wave frequency ω is close to the cyclotron frequencyω_(ce). Energy transfer from the electrons 36 to the wave is optimumwhen ω is slightly higher than ω_(ce) +k_(z) V_(z), where k_(z) is theaxial wave number of the electromagnetic wave and v_(z) is the axialvelocity of the electrons.

The phase synchronism enables the device to amplify, and since ω_(ce)=qB_(zo) /m, where q and m are the charge and relativistic mass,respectively, of an electron 36, amplification occurs at a wavelengthdetermined by the applied magnetic field B_(zo). Thus, to amplify a TE₀₁⁰ wave of frequency ω, a magnetic field B_(zo) is selected so thatω_(ce) +k_(z) v_(z) is slightly lower than ω.

The electron guns 16, drift tube 10, and waveguides 12 are placed withinthe bore of the solenoid 14 to facilitate the interaction between themagnetic field and the electron beam. The contour of the magnetic fieldmust be precisely shaped over the entire electron beam to provide theproper trajectory of the electrons 36. Such control is essential becauseof the great impact that small changes in the magnetic field have onboth the efficiency of the device and the operation of the electron gun16. The electron gun 16 may be placed externally of the solenoid 14, butin that case the contour of the magnetic field is much more gradual and,obviously, the length of the system is greater.

As the electron beam propagates in the drift tube 10 past the solenoid14, the beam expands radially and follows the lines of the magneticfield into the electron collector 28. The amplified TE₀₁ ⁰ wavecontinues to propagate axially until it leaves the drift tube 10 throughthe output pressure window 32. The deflection magnet 30 prevents strayelectrons from bombarding the output pressure window 32. The microwaveabsorber 34 prevents spurious oscillations and prevents microwave energyfrom entering the electron gun 16.

As the wave and beam propagate, amplification saturates because theelectrons become trapped in a phase of their cyclotron orbits relativeto the phase of the wave such that the transfer of energy from the beamto the wave no longer occurs. In order to inhibit the saturation, themagnetic field may be tapered (see FIG. 2) to change the phase of theelectrons, or the radius of the drift tube may be tapered to change thephase of the electric field of the wave.

The parameters relevant to the magnetron-injection electron gun 16 are:current I, voltage V, radius of the electron beam r_(o), and α=v.sub.⊥/v_(z). The parameters of the drift tube 10 are the radius r_(w) andlength L. The interaction of the electron beam and the wave requires aspecific magnetic field B_(zo) for the particular frequency ω of thewave.

To determine these parameters select the following:

a. 1.5<α<2.5 where 1.5 provides conservative design and 2.5 givesoptimum efficiency;

b. The mode of the travelling wave, preferably the TE₀₁ ⁰ mode whichwill be used in these calculations;

c. power output P_(o) ;

d. the harmonic s, preferably s=1, of the cyclotron frequency ω_(ce) ;and

e. the frequency ω of the wave to be amplified, and using a single -waveparticle simulation code, which employs the relativistic Lorentz forceequation in which the fields are those of the selected electromagneticmode (e.g., TE₀₁ ⁰) and the applied steady magnetic field B_(zo) and inwhich the frequency and amplitude of the electromagnetic mode areself-consistently evaluated using Maxwell's wave equation, calculate thelarge signal dynamics of the particle trajectories for an ensemble ofparticles and generate curves such as those in FIG. 6 (for which theTE₀₁ ⁰ mode, α=1.5, and s=1 were selected) which provide the values of Vand I for a maximum efficiency η at a given power output P_(o).

Wave amplification results from the interaction between the circularwaveguide mode whose frequency is given by,

    ω.sup.2 =k.sub.z.sup.2 c.sup.2 +ω.sub.c.sup.2  (1)

and the frequency of the cyclotron beam mode,

    ω=k.sub.z v.sub.z +qB.sub.zo /m                      (2)

where k_(z) is the axial wave number, c is the speed of light, and ω_(c)is the cutoff frequency of the wave, that is, the minimum frequency atwhich the wave will propagate in the drift tube 10.

In order to achieve high efficiency, it is desirable to select themagnetic field such that the two curves represented by equations (1) and(2) meet at a grazing angle, that is, with the group velocity (k_(z) c²/ω) of the waveguide mode nearly equal to the velocity (v_(z)) of theelectron beam.

Assume v_(z) is equal to the group velocity of the wave. Therefore,

    v.sub.z =(k.sub.z.sup.2 c.sup.2 +ω.sub.c.sup.2).sup.1/2 k.sub.z c.sup.2.                                                  (3)

The voltage V is selected from the curve of FIG. 6 and ##EQU1## wherem_(O) is the rest mass of an electron and ##EQU2## where α had beenselected as 1.5 to develop the curves of FIG. 6.

Solving, simultaneously, equations (4), (5), and (6) provide values forγ, v_(z) and v.sub.⊥.

The relativistic mass m of an electron appears in equation (2) and maybe determined by

    m=γm.sub.o.                                          (7)

Since ω, v_(z) and m are known and c and q are constants, solvingequations (1), (2) and (3) provides the values for k_(z), ω_(c) andB_(zo).

In practice, it may be necessary to tune the magnetic field B_(zo) byapproximately 4 percent from the value obtained above to provide theoptimum operation condition.

For a wave in the TE₀₁ ⁰ mode,

    r.sub.w =2π0.609c/ω.sub.c)

For maximum interaction between the electron beam and the TE₀₁ ⁰ wavethe radius r_(o) of the beam should equal the radius of the electricfield of the wave. Thus for a TE₀₁ ⁰ wave

    r.sub.o =0.48r.sub.w                                       (9)

The gain of the system is

    P.sub.o /P.sub.i =e.sup.2Γ.sbsp.L.sup.L              (10)

where P_(o) is the specified power output, P_(i) is the power input andis a known factor according to available driver radiation sources, e isthe base of the natural logarithm, L is the length of the drift tube 10and ##EQU3## where

    δω=|η.sub.b e.sup.2 Q(X)/6m.sub.0 ε.sub.0 |.sup.1/2                                        (12)

and η_(b) is the electron density averaged over a cross-section of thedrift tube and is therefore a function of the current I and radius r_(w)of the drift tube. Also, in equation (12) ##EQU4## where J₁ is theBessel function of the first kind order one. Solving equations (10)through (15) provides the length L of the drift tube.

The parameters of the magnetron-injection electron gun (I, V, r_(o), α,v.sub.⊥ and v_(z)), drift tube (r_(w) and L) and the magnetic fieldB_(zo) are thereby determined for amplifying a travelling wave of adesired mode and frequency ω.

Obviously more modifications and variations of the present invention arepossible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims the inventionmay be practiced otherwise than as specifically described.

What is claimed and desired to be secured by Letters Patent of theUnited States is:
 1. A gyrotron travelling-wave amplifier comprising incombination:wave-launching means for launching a travelling wave in apreferred mode at a selected frequency ω; beam-producing means forforming and propagating an annular beam of electrons at relativisticspeeds along a path; a fast-wave structure, coupled to saidwave-launching means and said beam-producing means, wherein said waveand said beam propagate and interact for transferring energy from saidbeam to said wave, thereby amplifying said wave; and means for forming amagnetic field B about said beam-producing means and fast-wavestructure, said magnetic field having a uniform axial component B_(zo)in the region of the fast-wave structure and said magnetic field havingboth an axial component B_(zg) and a radial component B_(rg) about saidbeam-producing means, said axial B_(zg) and radial B_(rg) componentsbeing chosen so as to form a beam of electrons with a velocity componentv.sub.⊥, transverse to the axial direction, for causing said electronsto form cyclotron orbits about the axial lines of said magnetic fieldB_(zo), said magnetic field B_(zo) being chosen for causing saidelectrons to gyrate in said orbits at a cyclotron frequency ω_(ce) givenby ω_(ce) ×qB_(zo) /m, where q and m are the charge and relativisticmass, respectively, of an electron, and where B_(zo) is of a magnitudesuch that said selected frequency ω of said travelling wave is slightlyhigher than qB_(zo) /m+k_(z) v_(z), where k_(z) is the axial wave numberof the travelling wave and v_(z) is the axial velocity of the electrons.2. A gyrotron travelling-wave amplifier as recited in claim 1, whereinsaid fast-wave structure includes microwave absorbing material andmicrowave mode traps for stabilizing the operation as an amplifier inthe desired mode.
 3. A gyrotron travelling-wave amplifier as recited inclaim 1, wherein said means for forming a magnetic field provides atapered mangetic field near the output end of said fast-wave structurefor changing the phase of the electrons of said beam relative to thephase of the electric field of said wave for optimizing the transfer ofenergy from said beam to said wave.
 4. A gyrotron travelling-waveamplifier as recited in claim 1, wherein said beam-producing meanscomprises a magnetron-injection gun.
 5. A gyrotron travelling-waveamplifier as recited in claim 1, wherein said wave-launching meanscomprises waveguides for conducting waves of equal amplitude andopposite phase and for coupling to said fast-wave structure forlaunching a wave therein.
 6. A gyrotron travelling-wave amplifier asrecited in claim 2, wherein said fast-wave structure is tapered near theoutput end for changing the phase of the electric field of said waverelative to the phase of the electrons of said beam for optimizing thetransfer of energy from said beam to said wave.
 7. A gyrotrontravelling-wave amplifier as recited in claim 3, wherein said means forforming a magnetic field includes a superconducting solenoid.
 8. Agyrotron travelling-wave amplifier as recited in claim 5, wherein saidwaveguides are of rectangular cross-section.
 9. A gyrotrontravelling-wave amplifier as recited in claim 6, wherein said fast-wavestructure comprises a drift tube.
 10. A gyrotron travelling-waveamplifier as recited in claim 8, wherein said fast-wave structure is ofcircular cross-section.
 11. a gyrotron travelling-wave amplifier asrecited in claim 10, wherein said waveguides are coupled to saidfast-wave structure at points approximately diametrically apart.
 12. Amethod for optimizing the parameters of the gyrotron travelling-waveamplifier of claim 1 for amplifying a travelling wave of a desired modeand frequency comprising the steps of:selecting a magnetron injectiongun which provides an annular beam of relativistic electrons, whichgyrate in cyclotron orbits at a cylotron frequency ω_(ce), said beamhaving a velocity ratio 1.5<α<2.5 as defined by α=v.sub.⊥ /v_(z) wherev.sub.⊥ is the transverse velocity of the electrons and v_(z) is theaxial velocity of the electrons; selecting a mode of a travelling wavewhich is to be amplified; selecting the frequency ω of said travellingwave; selecting an applied magnetic field B_(zo) ; selecting a poweroutput P_(o) ; selecting a harmonic s of the cyclotron frequency ω_(ce); using a single-wave particle simulation code, which employs therelativistic Lorentz force equation in which the fields are those of theselected travelling wave mode and the applied magnetic field B_(zo) andin which the frequency and amplitude of the travelling-wave mode areself-consistently evaluated using Maxwell's wave equation, calculate thelarge signal dynamics of the particle trajectories for an ensemble ofparticles for generating values for voltage V and current I for amaximum efficiency at the power output P_(o) ; solving the followingequations simultaneously; ω² =k_(z) ² c² +ω_(c) ² where ω is thefrequency of the wave mode, k_(z) is the axial wave number, c is thespeed of light, and ω_(c) is the cutoff frequency of the wave, ω=k_(z)v_(z) =qB_(zo) /m where ω is the frequency of the cyclotron beam mode, qand m are the charge and relativistic mass, respectively, of anelectron, and B_(zo) is the applied axial magnetic field about saiddrift tube,

    v.sub.z =(k.sub.z.sup.2 c.sup.2 +ω.sub.c.sup.2).sup.1/2 k.sub.z c.sup.2,

V=(γ-1)m_(o) c² /q, where V is selected from the values determined bysaid simulation code; ##EQU5## and m_(o) is the rest mass of an electronas defined by

    m.sub.o =m/γ,

and

    α=v.sub.195 /v.sub.z,

said equations providing the values for γ, v_(z), v.sub.⊥, k_(z), ω_(c),B_(zo) and r_(w) and r_(o) where r_(w) is the radius of the drift tubefor a given wave mode, as for example r_(w) =2π (0.609c/ω_(c)) for awave in the TE₀₁ ⁰ mode, and r_(o) is the radius of said electron beamfor a given wave mode, as for example r_(o) =0.48 r_(w) for a wave inthe TE₀₁ ⁰ mode; tuning said value of the magnetic field B_(zo) byapproximately four percent; solving the following equationssimultaneously: P_(o) /P_(i) =e²Γ.sbsp.L^(L) which is the gain of thesystem and where P_(i) is the power input, e is the base of the naturallogarithm, L is the length of the drift tube, and ##EQU6## whereδω=|η_(b) e² Q(X)/6m_(o) ε|^(1/2) where η_(b) is the electron densityaverage over a cross-section of the drift tube, ##EQU7## Q(X)=(X⁻² -1)dJ₁ ² (X)/dX, and W(X)=[J₁ (X)]² where J₁ is the Bessel function of thefirst kind order one, said equations providing the value of the length Lof the drift tube.